For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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0
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3answers
48 views

getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
1
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3answers
18 views

Finding Angle Measures

An A-frame house is 40 feet high and 30 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
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1answer
32 views

What's the difference between these rotations?

1) Each point on the coordinate plane is rotated $\theta$ degrees about the origin. 2) Each point $P$ with the coordinates $(x,y)$ is rotated $\frac{\pi}{4}$ radians about the origin. The answer ...
0
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2answers
58 views

spherical triangle: law of sines

Given plane triangle ABC it is well known that the common value of the ratios appearing in the law of sines is equal to the diameter of the circle which passes through the three vertices. ...
1
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2answers
59 views

Describing all points 4000 miles from the north pole

I'd like to describe all of the points on the Earth's surface that are exactly 4000 miles from the North Pole. I know that this will eventually give me an equation for a circle; I want to find that ...
0
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0answers
35 views

Continuous, smooth derivative for two “stitched” ellipses

This is something of a whim, but it won't leave me. Consider two ellipses, P and Q, with $P(a<b)$, $Q(b<c)$ and $a<b<c$ (not $<<$). Is it possible that, by cutting P along its major ...
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2answers
37 views

How to find the third vertex of an isosceles triangle given 2 points.

This is the full problem: The points $A(5,1)$ and $B(-3,6)$ represent one of the equal sides of an isosceles triangle. Determine one of the possible points that would represent the third vertex of the ...
-2
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1answer
19 views

hard isosceles triangle/isosceles trapezoid question

Triangle ABC sits right on top of trapezoid DBCE. BC is parallel to DE. Triangle ABC's area is half of the area of trapezoid DBCE. What's the ratio of AC to AE?
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0answers
72 views

What if the cow could fly?

See grazing cow. Now keep the restriction that the length of the rope is $l\leq\pi r$ where $r$ is the radius of the barn, (I like to think of this as a goat tied to a silo) but now suppose the cow ...
1
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0answers
19 views

Is it possible to reconstruct a triangulation from its $1$-skeleton?

Let's restrict to triangulations $T$ of compact and closed smooth manifolds $M$ with $\dim M=2,3$. Such a triangulation is a PL manifold homeomorphic to $M$ which geometric realization is a simplicial ...
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2answers
41 views

Find the radius of four congruent circles inside a right triangle

Below is a homework assignment I'm working on, along with a correct method for solving it and what appears to be an incorrect method. I'm hoping someone could explain what is wrong with the second ...
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3answers
88 views

Area of the field that the cow can graze.

How do we find the area that the cow can graze? The question goes as follows-- There is a circular barn house surrounded by a huge grazing field. A cow is tied to the rope ($AB$) at the end $A$ as ...
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votes
1answer
26 views

Why is it a borel set on the boundary of the unit ball of $E^n$?

Given $C$ convex body (compact convex set with non-empty interior points) in $E^n$ symmetric about the origin and containing the unit ball. Let $A(r)$ denote ,for every real $r >1$, the subset of ...
2
votes
1answer
103 views

Length minimizing curves are geodesic segments

I have a metric space $(X,d)$, a geodesic arc is defined to be a continuous function $\gamma : [a,b] \rightarrow X$, $a < b$, which is (globally) distance preserving and geodesic segments are ...
1
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1answer
36 views

what is the meaning of asphericity of convex set in a linear normed space?

I am trying to understand the definition of spherical to within $\epsilon$ for a convex body in a linear normed space, as given in Aryeh Dvoretzky's paper [1] (section 2, page 203): A convex set ...
1
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1answer
42 views

An angular inequality

In a triangle $ABC$, let $D$ and $E$ be the feet of the angle bisectors of angles $A$ and $B$, respectively. A rhombus is inscribed into the quadrilateral $AEDB$ (all vertices of the rhombus lie on ...
0
votes
3answers
36 views

Inscribe a rectangle inside an ellipse

A rectangle is to be inscribed inside a horizontal ellipse (whose major or minor axis is parallel to x axis). Is the horizontal orientation of the rectangle (two sides parallel to x axis) the only ...
0
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1answer
52 views

If you know 2 sides of the triangle, wha is the third side?

I understand why A & C are correct but I don't get how E is a possible length since whatever number I plug in for x I get a number greater than 5x+5...
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1answer
44 views

SAT geometry and algebra [closed]

QI: Segment XY is the diameter of a circle. Point Z is placed on the circle such that the length of XZ is 6 and the length of ZY is 8. What is the area of the circle? (A) 10π (B) 25π (C) 36π (D) ...
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0answers
37 views

Generalizations of functions

I'm trying to collection examples of mathematical entities that are generalizations of functions. The use of the word "generalization" here doesn't need to be strict, as in every function is an $X$ ...
1
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0answers
39 views

Tangent bundle is orientable

I am having some trouble finishing a proof that the tangent bundle of any manifold is orientable. What I've done so far is calculate the transition function between two standard charts on the bundle. ...
2
votes
2answers
54 views

Primary school math regarding circles [closed]

----------//-----------------------------------__________ Please see the figure below the question is in the ...
2
votes
2answers
36 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
2
votes
3answers
63 views

Are there circles in $\mathbb{R}^d$ taking no rational values?

I recently stepped over a little detail in a thesis I still wonder about. If one looks at $\mathbb{Q}$, then it is dense in $\mathbb{R}$, and we have no problem finding real numbers that don't belong ...
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votes
3answers
21 views

point on a line and distance from a point

I have point(x1,y1) and point(x2,y2) these are end point of line and point(m,n) is a point. How can i find Point(a,b) which lies on the line ,that is the shortest path from point(m,n) to the line
2
votes
0answers
32 views

Packing circles in circle vs semicircle vs quarter of circle

Consider $N$ disjoint circles with radius $1$ packed into a larger circle $C$. Let $R$ be the smallest possible radius of $C$, allowing the best packing density. Now take the $N$ unitary circles ...
0
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3answers
35 views

For a line how to find $y=mx+c$ if $x_1,y_1$ and $x_2,y_2$ in hand

How can I find $y=mx+c$ for a line? I have only two end points $x_1,y_1$ and $x_2,y_2$.
0
votes
1answer
20 views

Find a projectivity to create a graph.

I have the tetrahedron {xyzt=0} in projective space with homogeneous coordinate (x,y,z,t). I need to create a graph but the tetrahedron in affine coordinate is {xyz=0} and I can't visualize the ...
0
votes
0answers
26 views

how to find the optimal path for a rescue robot?

The rescue robot is searching signals in a huge rectangle area without obstacles. We assume: - only one signal source in the area in a constant location. - the robot is small enough to be regard ...
2
votes
4answers
65 views

How many pieces of information are needed to determine a triangle?

Typically 2 sides and 1 angle need to be given in order to determine a unique triangle. Alternatively 1 side and 2 angles, or the Cartesian coordinates of three vertices, or the area, base, and ...
1
vote
1answer
33 views

Calculating tangent point on arc from a known arc point

I am trying to figure out how to calculate a tangent point on arc given a point on the arc (the midpoint) and the arc's radius. I have a diagram: The two red lines that come to a point are the ...
2
votes
1answer
90 views

Calculate the areas in a circle

Short: I want to calculate the areas drawn in this picture: The coordinates P00, P10, P01, P11 and Pdata are given Long: I am a programmer and want to calculate these areas, but unfortunately I am ...
1
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0answers
20 views

What's the name for a polygon with exactly two sets of side lengths?

Is there a name for the shape similar to a regular polygon, but using exactly $2$ side lengths (or $n$ side lengths) instead of one side length?
1
vote
2answers
26 views

Geometry parallelogram help

ABCD is a parallelogram with side AB=12 cm. Its diagonal AC and BD are of lengths 20 cm and 16 cm respectively. Find the area of parallelogram ABCD. I tried, Area of parallelogram=1/2*product of ...
0
votes
2answers
12 views

A cycloid that goes through the beginning and through a general point

Parametric equations of the general cycloid through the beginning $(0,0)$ are $$x(t)=\frac{2t-\sin2t}{2d}$$ $$y(t)=\frac{1-\cos 2t}{2d}$$ How can we determine $d$ such that the cycloid goes through ...
0
votes
1answer
17 views

Divide-and-conquer on a rectilinear polygon

A rectilinear polygon can be characterized by its cover number - the smallest number $k$ such that the polygon can be covered by $k$ possibly overlapping squares. For example: For a square, $k=1$. ...
39
votes
17answers
2k views

How to create circles and or sections of a circle when the centre is inaccessible

I am doing landscaping and some times I need to create circles or parts of circles that would put the centre of the circle in the neighbours' garden, or there are other obstructions that stop me from ...
0
votes
1answer
27 views

Unique Euclidean isometry between affinely independent points

Let $u_0,\dots,u_n$ be vectors in $\mathbb{R}^n$ such that $u_1-u_0,\dots,u_n-u_0$ are linearly independent and similarly let $v_0,\dots,v_n$ be vectors in $\mathbb{R}^n$ such that ...
0
votes
1answer
56 views

Right Triangles Geometry Proof

Quadrilateral WXYZ has right angles at angle W and angle Y and an acute angle at angle X. Altitudes are dropped from X and Z to diagonal WY, meeting WY at O and P. Prove that OW = PY.
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2answers
31 views

Derive formula for coordinates of internal and external centers of similitude.

Given 2 circles $(x - x_1)^2 + (y - y_1)^2 = r^2$ and $(x - x_2)^2 + (y - y_2)^2 = r'^2$ (with radii $r, r'$) coordinates of the internal and external centers of similitude $C_i, C_e$ are given by ...
0
votes
1answer
11 views

Calculate position of N points around given point in 3d space?

Sorry if I used wrong words - English is not my native language, and I never actually studied geometry. For a project I'm working on, I need to calculate set of points, that: are in given, ...
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0answers
29 views

Angular displacement/speed of a rotating sphere

I really don't know how to obtain "true angle" between two points on a sphere in rotation with fixed center. For exemple, I have points $P_i$ with spherical coordinates representing a rotation : ...
-4
votes
1answer
34 views

SAT and deceptive graphs (figure not drawn to scale)

Question I. Figure may be found at: https://www.dropbox.com/s/skkkx9ydnrsdq8o/20140709_153701.jpg The Venn diagram above represents the 20 students who took one or more of the three available art ...
0
votes
1answer
15 views

How would I find the scale factor of a dilated figure on a coordinate plane?

The above question is pretty simple, and I used common sense to figure out that the coordinates (3, -7) is the answer, since it is the only viable spot. I was wondering how I would find the scale ...
3
votes
2answers
91 views

Triangle problem - finding the angle

Please look at the following figure: All the angles are in degrees. I have to find $x$. I am really no good at solving geometry problems. I tried to search the internet for similar problems and ...
1
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0answers
35 views

How to prove law of tangent using vector method

I saw the proof of law of tangent using trigonometry. There are also proofs for law of sine and cosine using vector methods. Can somebody tell me how to get the proof of law of tangent using vectors? ...
0
votes
3answers
20 views

Parallelogram help

In a parallelogram ABCD, AB=8 cm, BC=5 cm, perpendicular from A to DC=3 cm. Find the length of the perpendicular drawn from B to AD. I am not quite sure how to draw the diagram. Is this the way I ...
0
votes
0answers
17 views

Change of one coordinate axes to another.

Let suppose i have a acceleration values along the $x,y,z$ axis and the $3$ angles ($\alpha$ (rotation around $x$ axis), $\beta$ (rotation around $y$ axis), $\gamma$ (rotation around $z$ axis)) to ...
1
vote
0answers
54 views

How to calculate one side of an arbitrary square

Firstly, sorry for my silly or simple question, and sorry for my bad English. I have an arbitrary square which is like this: Maybe it can be solved with Pythagoras by splitting into two triangle Can ...
-1
votes
1answer
38 views

Pythagoras theorem and ratios of sides

In a right angle LAB angle L is right angle and AM is perpendicular to AB. Prove that LA^2 : LB^2 = AM : MB. This can be proved using similar triangle principles. But I am interested to prove this ...